Electric charge on q?

In summary, the net force on the 1.0 mC charge is zero in this diagram. To determine the sign and magnitude of the unknown charge q, the force required by "q" on the middle particle must be calculated. By considering the forces between q and the bottom two particles, it can be determined that q must place a force of 2Fy in the -y direction on the middle particle. Using this information, the charge of "q" can be calculated using the equation q = (2Fy)(r^2)/(k)(Q1) where Q1 is the middle particle. However, it should be noted that this approach may not be accurate as it does not take into account the forces between q
  • #1
RyanBruceX
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Homework Statement



In this diagram, the net force on the 1.0 mC charge is zero. What is the sign and magnitude of the unknown charge q? Please see attached photo.
[/B]

Homework Equations


F = KQ1Q2/r^2[/B]

The Attempt at a Solution



I have approached this by first determining the force required by “q” on the middle particle to maintain the system in its current position. Because the 2 bottom particles cancel in the “x” direction the combined force they place on the middle particle is 2Fy? And so “q” must also place a force of 2Fy but in the -y direction on the middle particle. So by this rationale I should be able to calculate the charge of “q” using q = (2Fy)(r^2)/(k)(Q1) where Q1 is the middle particle.
q = (8.65 x 10^6 N)(0.0009 m^2) / (9.0 x 10^9 N M2/C2)(1.0 x 10^-3 C) = 8.65 x 10^-4 C positive charge?

I am assuming I do not have to use the vector method to determine the force of q because it also has equal components in both the - and + x directions which cancel. So net force is just in the y direction and this is used to calculate the charge?

The magnitude of this charge seems low to me, I would have expected a more symmetrical charge. Should I be considering the forces between q and the bottom two particles?[/B]
 

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  • #2
Misread the question. Please ignore my previous post.
 
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  • #3
Your work looks fine. Note that q doesn't just produce "equal components in both the - and + x directions which cancel", it produces NO components in the in those directions when it acts on the 1mC charge (or, technically, they are zero valued).

The charge may seem small but keep in mind it is closer to the 1mC charge than the others and the force varies as the inverse square of the separation.
 
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  • #4
Thank you very much! I forgot about this being a "fixed position" question. My thoughts on the -/+ x direction components for "q" were based on the forces between "q" and the bottom particles. Would they not also produce a force at an angle towards "q" as they do towards the middle particle? I just have a hard time conceptualizing this problem, my solution was approached by breaking the system up. Focusing on the effect of the bottom particles on the middle particle only, and then focusing on the equal and opposite effect of "q" on the middle particle (forgetting fixation). So while I may have come up with the right answer it was wrong reasoning. When I look at the system as a whole It would seem to me that all the particles should exert a force on each other and so "q" should feel a force of 2Fy (using q and 2 mC as charges, and the distance q to the bottom particle) plus the Force of the middle particle on q. Unless somehow 2Fy using 1 mC and 2 mC and the distance from the bottom to middle provides the same magnitude...
 
  • #5


I would approach this problem by first considering the fundamental principles of electric charge. Electric charge is a property of matter that causes it to experience a force when placed in an electric field. This force is described by Coulomb's law, which states that the force between two charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this scenario, we have a system of three charges, with two of them being equal and opposite and the third one being unknown. The net force on the middle charge is zero, which means that the forces exerted by the two bottom charges must cancel out. This can only happen if the two bottom charges have equal magnitudes and opposite signs. Therefore, we can conclude that the unknown charge q must also have an equal magnitude but opposite sign to the bottom charges.

Using Coulomb's law, we can calculate the magnitude of the unknown charge q by equating the forces between q and the bottom charges. Since the forces are equal in magnitude but opposite in direction, they will cancel out and the net force on the middle charge will be zero. Therefore, the magnitude of the force between q and each of the bottom charges is equal to half of the force between the bottom charges. This can be expressed as:

F_q = (1/2) * F_bottom

Substituting the values given in the problem, we can solve for the magnitude of q:

F_q = (1/2) * (8.65 x 10^6 N)
F_q = 4.325 x 10^6 N

Now, we can use Coulomb's law to calculate the magnitude of q:

F = K * (q1 * q2)/r^2
4.325 x 10^6 N = (9.0 x 10^9 N*m^2/C^2) * (q * 1.0 x 10^-3 C)/(0.0009 m^2)
q = (4.325 x 10^6 N * 0.0009 m^2)/(9.0 x 10^9 N*m^2/C^2)
q = 4.83 x 10^-4 C

Based on this calculation, the magnitude of the unknown charge q is 4.83 x 10^-4 C, which is slightly higher than your initial estimate. This is because we need to take
 

1. What is electric charge?

Electric charge is a fundamental physical property of matter that describes the amount of electric force an object experiences in an electric field.

2. What are the two types of electric charge?

The two types of electric charge are positive and negative. Positive charges are associated with protons and negative charges are associated with electrons.

3. How is electric charge measured?

Electric charge is measured in units called Coulombs (C). One Coulomb is equivalent to the charge of approximately 6.24 x 10^18 electrons.

4. What is the symbol for electric charge?

The symbol for electric charge is q. It is often used in equations to represent the amount of charge an object possesses.

5. How does electric charge interact with other objects?

Electric charge can interact with other objects through the electromagnetic force. Like charges repel each other while opposite charges attract each other.

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